The most common reason a washing machine stops spinning is a broken belt. However they can also stop spinning if the motor burns up. If you can move it enough to see into the back of the machine a broken belt is usually easy to spot. If the belt is intact you will probably need a repairman to diagnosis the problem. If you are not overly handy you will need the repair guy anyway. Hope its a Maytag, that poor guy gets so lonely.
A common problem causing a washing machine to not spin, is the cycle knob is not pulled out. Sometimes, when you add fabric softener, the lid inadvertently pushes the knob in and causes it not to progress to the spin cycle.